Then I wanted to test restores - The Veeam server showed the AD Explorer, so it knows its an AD server. But the AD Explorer starts up with an error saying "The specified database cannot be opened on this OS version. (JetError -512, JET_errBadLogVersion, Version of the log file is not compatible with Jet version)

Does the Veeam Explorer have to be Windows 2008 for this to Work?
I know the Veeam Explorer should be installed on the same or newer OS version as AD, but in my case Veeam Console and Veeam Explorer are installed in a newer version.

Hi Stefano, there were issues with opening backups of previous versions of Active Directory on Windows Server 2016, so I recommend installing Veeam B&R console on one of the earlier versions to perform restores.

There's no matrix as the general rule is to use Veeam Explorer for Active Directory installed on the same or newer Windows version as Active Directory itself, as you've mentioned. We're working on addressing all the issues so that this rule remains applicable in all cases. And, btw, we couldn't reproduce this internally, Windows 2008 DC database successfully opened on Windows Server 2016 in our lab, so I'd appreciate if you could contact support for a closer look. Thanks.